Proving statements about angles BIG IDEA: Reasoning and Proof ESSENTIAL UNDERSTANDING Given information, definitions, properties, postulates, and previously proven theorems can be used as reasons in a proof. MATHEMATICAL PRACTICE Construct viable arguments and critique the reasoning of others. Proving statements about angles

Getting Ready A quilter wants to duplicate this quilt but knows the measure of only two angles. What are the measures of angles 1, 2, 3, and 4? How do you know?

Math Background In a sense, proofs are problems in which the answer is already known and the focus is on demonstrating how the answer is derived using principles of deductive reasoning and related definitions, properties, postulates, and theorems. In writing proofs, you will communicate your reasoning clearly to others using the two-column proof.

Theorems Right Angle Congruence Theorem Congruent Supplements Theorem All right angles are ____________________ Congruent Supplements Theorem If two angles are ______________________ of the same angle (or of congruent angles), then the two angles are __________________ Congruent Complements Theorem Vertical Angles Theorem Vertical angles are ____________________ Theorem: If two angles are _______________ and ____________________, then each is a ____________ angle

EX 1 Find the measures of the angles in the diagram given.

EX 2 Complete the statements given that 1. 2. 3. 4. 5. 6.

EX 3 Given: Prove: Statements Reasons

EX 4 Given: Prove: Statements Reasons 1. 2. 2 3. 4.

EX 5 Given: Prove: Statements Reasons 1 2 2 Definition of Supplementary Angles 3 4 4 Given 5 6 6 Subtraction Property 7

2.6 p. 113 10, 12 – 18 all, 20 – 30 evens, 33 – 36 all, 38 – 45 all 26 questions